Short-Term Load Forecasting: Similar Day-Based Wavelet Neural Networks

muscleblouseAI and Robotics

Oct 19, 2013 (3 years and 9 months ago)

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Short
-
Term Load Forecasting:
Similar Day
-
Based Wavelet Neural
Networks

Ying Chen, Peter B.
Luh
,


Fellow, IEEE,



Che

Guan,
Yige

Zhao


Laurent D. Michel

Matthew A.
Coolbeth
,

Peter B.
Friedland

Stephen J.
Rourke
,


Senior Member, IEEE


World Congress on Intelligent Control and Automation, July 2008

IEEE TRANSACTIONS ON POWER SYSTEMS, Feb 2010

Outline


Background


Similar Day
-
Based Wavelet Neural Networks


Weekday Index and Weather


Similar Day
-
Based Load Input Selection


Decomposition Input Load


Neural Networks


Testing Results


Conclusion

Background


In deregulated electricity markets, short
-
term load
forecasting is important for reliable power system
operation, and significantly affects markets and their
participants.


Representative short
-
term load forecasting method


Regressions


Similar day methods


Neural networks

Similar Day
-
Based Wavelet Neural
Networks


Similar day
-
based wavelet neural network
method (SIWNN) is developed to predict
tomorrow’s load.


Consists of
similar
-
day based input selection
,
wavelet decomposition
, and
neural networks.

Similar Day
-
Based Wavelet Neural
Networks


Main idea is to select the similar day’s load as the
input load, apply wavelet to decompose it into low
and high frequency components, and then use
separate networks to predict the two components
of tomorrow’s load.

Similar Day
-
Based Wavelet Neural
Networks


Load affecting factors


Weekday Index


Weather


Similar Day
-
Based Load Input Selection


Decomposition Input Load


Neural Networks


Weekday Index


Weekday index is an important load affecting
factor in view that different days of a week
generally have different load shapes

Weather
-

winter


Weather information used in SIWNN includes wind
-
chill
temperature, humidex, wind speed, cloud cover, and
precipitation.


Temperature that is felt could be much lower than air
temperature in winter cause of wind, so
wind
-
chill
temperature
is used for winter.



T
wc
:wind
-
chill temperature
T
a
:air

temperature
v
:wind speed

Weather
-

winter


Scatter plot of load versus
T
wc






Convert to a near linear pattern by processing with
the V
-
shaping function:





Weather
-

summer


The combined effects of heat and humidity cause
high level of discomfort in summer. Therefore,
humidex

that measures the combined effect of
heat and humidity is used for summer

H
:humidex
T
a
:air

temperature
D
:dew point

Weather
-

summer


Also Convert to a near linear pattern by V
-
shaping
function:





Similar Day
-
Based Load Input
Selection


Historical load is usually used as input for neural
network based prediction.


Common practice is to use the most recently
available load, like the load of yesterday, and the
load of one week ago with the same weekday index.

Similar Day
-
Based Load Input
Selection


Similar day selected is required to have the same
weekday index and similar weather to that of
tomorrow, and also required to have its day
-
of
-
a
-
year index within a neighborhood of that of
tomorrow to avoid seasonal variations.

f

:tomorrow (
the forecasted
day)

i

:historical day

w :
weather factor



(wind
-
chill in winter, humidex in summer)

Similar Day
-
Based Load Input
Selection


Scatter plot and correlation coefficient of common
and proposed methods

Correlation coefficient
= 0.67

Correlation coefficient
= 0.95

Common (versus yesterday)

Proposed (versus similar day)

Decomposition Input Load


Daubechies wavelets are good for load forecasting
since they are orthogonal wavelets, and will not
cause information loss in the frequency domain.


In SIWNN, Daubechies 4 wavelet (Db4) is used to
decompose the input load into a low frequency
component and a high frequency component.

Decomposition Input Load


L is the scaling function for Db4 used to filter out high
frequency component from the selected similar day’s load.


Down
-
sampling: Reduce data volume by dropping odd
indexed data points


Up
-
sampling: Pad zeros to the down
-
sampled data so as to
recover data length


Low
-
pass filter: Remove distortion caused by up
-
sampling.

Decomposition Input Load


Wavelet decomposition result for New
England,2006





Zoom in the original and low frequency for some
hours

Neural Networks


Two three
-
layer perceptron networks are
separately used for the low frequency component
and the high frequency component.


Inputs are selected based on testing experience.

Neural Networks


The two networks are first trained by using historical actual
data, with the similar day
-
based selection criteria applied to
each day in the training period.


Training process terminates when the training error is less
than a specified threshold. To avoid over
-
fitting, for each
network, number of hidden neurons, input selection, and
threshold value for terminating training are determined
based on extensive testing.


Predictions generated by the
two networks are added up to
be tomorrow’s forecasted load
.

Testing results


Three examples are presented below.


Example 1: Uses a classroom
-
type problem to
examine the value of using wavelet decomposition.


Example 2: Predicts New England 2006 load,
demonstrates the values of wind
-
chill temperature,
humidex, and weather preprocessing, and examines
sensitivity of prediction to weather forecasting errors.


Example 3: Predicts New England 2007 load, and
examines the effects of using wavelet
decomposition, similar day’s load, and
supplemental load on prediction accuracy

Example 1


Consider a signal:



Five hundred noisy data set were
randomly generated for training




Object is to find
y(t),
t=501~520

Example 1


Our method SIWNN and the standard NN method
that uses a single neural network without wavelet
decomposition are tested.







MAE is 0.86 for SIWNN, and 2.89 for the standard
NN method

Example 2


Case 1


This example predicts New England 2006 load,
and includes four cases.


Case 1: Compares using wind
-
chill temperature
versus using air temperature

Example 2


Case 2


Case 2: Compares using humidex versus using dew
point



Example 2


Case 3


Case 3: SIWNN is used to with and without data
preprocessing(v
-
shaping wind
-
chill temperature and
humidex)






Effects of the preprocessing on neural network training
speed are also examined by comparing the training iteration
numbers(low, high) frequency


With processing (700, 1230) iterations


Without processing (1540, 3127) iterations

Example 2


Case 4


Case 4: SIWNN and the standard NN method are
both tested by using actual weather and predicted
weather. SIWNN is
less sensitive to weather
forecasting errors
as compared with the standard
NN method.

Example 3


Case 1


This example predicts New England 2007 load, and
includes four cases.


Case 1: SIWNN and a single network without
wavelet decomposition are compared.

Example 3


Case 2


Case 2: Prediction of
high frequency load
is
examined with accuracy measured by MAE

Example 3


Case 2


To examine the value of precipitation, the high
frequency network is tested with and without
precipitation.

Example 3


Case 3


Case 3: Compares using the similar day’s load
versus the standard practice of using the most
recent load

Example 3


Case 4


Case 4: SIWNN is used with and without the
supplemental load(today’s predicted load) to
examine its value.

Conclusion


This paper presents a framework that combines similar day
selection, wavelet decomposition, and neural networks to
forecast tomorrow’s load.


Key idea is to use similar day’s load supplemented by
today’s predicted load as input load, and use a synergistic
combination of wavelet decomposition and neural networks
to capture key features of load at low and high frequencies


This method has been extended for holiday load forecasting,
and very short
-
term load forecasting.